Exponentially correlated Hylleraas-configuration-interaction non-relativistic energy of the 1S ground state of the helium atom

Published

July 26, 2021

Author(s)

James S. Sims, Maria B. Ruiz, Bholanath Padhy

Abstract

A generalization of the Hylleraas-configuration-interaction method (Hy-CI) first proposed by Wang, et al. , the Exponentially Correlated Hylleraas-configuration-interaction method (E-Hy-CI) in which the single rij of an Hy-CI wave function is generalized to a form of the generic type rνij e−ωij rij , is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior both in the vicinity of the r12 cusp and as r12 goes to infinity; this work explores whether wave functions containing both linear and exponential rij factors converge more rapidly than either one alone. The method of calculation of the two-electron E-Hy-CI kinetic energy and electron repulsion integrals in a stable and efficient way using recursion relations is discussed, and the relevant formulas are given. The convergence of the E-Hy-CI wave function expansion is compared with that of the Hy-CI wave function without exponential factors, demonstrating both convergence acceleration and an improvement in the accuracy for the same basis. This makes the application of the E-Hy-CI method to systems with N > 4, for which this formalism with at most a single rνij e−ωij rij factor per term leads to solvable integrals, very promising. E-Hy-CI method variational calculations with up to 10080 expansion terms are reported for the ground 1S state of the neutral helium atom, with a resultant nonrelativistic energy of -2.9037 2437 7034 1195 9831 1084 hartrees (Ha) for the best expansion.

Citation

International Journal of Quantum Chemistry

Pub Type

Journals

Download Paper

https://doi.org/10.1002/qua.26470

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Keywords

Explicitly correlated Hylleraas-Configuration Interaction, E-Hy-CI variational calculation, high precisionvariational calculation, helium ground state calculation, helium ground state energy.

Citation

Sims, J. , Ruiz, M. and Padhy, B. (2021), Exponentially correlated Hylleraas-configuration-interaction non-relativistic energy of the 1S ground state of the helium atom, International Journal of Quantum Chemistry, [online], https://doi.org/10.1002/qua.26470, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=930692 (Accessed October 7, 2025)